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The dynamic instability of dispersed price equilibria

The dynamic instability of dispersed price equilibria,10.1016/j.jet.2011.05.014,Journal of Economic Theory,Ratul Lahkar

The dynamic instability of dispersed price equilibria   (Citations: 5)
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We adopt an evolutionary framework to explain price dispersion as a time varying phenomenon. By developing a finite strategy analogue of the Burdett and Judd (1983) price dispersion model, we show that all dispersed price equilibria are unstable under the class of perturbed best response dynamics. Instead, numerical simulations using the logit dynamic show that price dispersion manifests itself as a limit cycle. We verify that limit cycles persist even when the finite strategy model approaches the original continuous strategy model. For a particularly simple case of the model, we prove the existence of a limit cycle.
Journal: Journal of Economic Theory - J ECON THEOR , vol. 146, no. 5, pp. 1796-1827, 2011
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    • ...But it will be shown in this paper that (at least for low dimensional games) the Shapley polygon is unique. A similar problem is addressed in [13]...
    • ...In contrast to Varian [18] discrete prices are used and a dynamical approach is taken in this paper. I use a simplification as in [13]...
    • ...But as simulations in [13] show the number of customers who check more than two prices goes to zero under learning behaviour...
    • ...[13], where prices are given as an arithmetic sequence...
    • ...This mono-cyclicity result can be found in [1, 8 ]o r [13]...
    • ...In [13] a uniform price distribution {0, 1 , 2 ,..., 1} is used to construct a finite approxima-...
    • ...tion of S =[ 0, 1]. But whenever there is a positive number of uninformed customers there are dominated strategies, so the game can always be analysed by looking at a restricted game. I follow Example 6.2 from Lahkar [13]...
    • ...This is also found in [13] for perturbed best response dynamics...

    Martin Hahn. An Evolutionary Analysis of Varian’s Model of Sales

    • ...5 See especially Hopkins and Seymour (2002) and Lahkar (2007), who argue that mulitiplicity of prices in models of price dispersion (Burdett and Judd (1983), Varian (1980)) is the result of cyclical rather than equilibrium behavior...

    William H. Sandholmet al. Survival of dominated strategies under evolutionary dynamics

    • ...Clearly, the vector eld generated by the two operators in (27) and(28) is identical to the vector...
    • ...We write R = R1, as in (27), for the replicator operator in the symmetric case.24...

    Ratul Lahkaret al. Reinforcement Learning in Large Population Models: A Continuity Equati...

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